Implements dpctl.tensor.repeat, dpctl.tensor.tile

[ndgrigorian]

This pull request implements dpctl.tensor.repeat, as well as changes necessary to include it in dpctl.

This function repeats the elements of an array along a given axis, and accepts integers, tuples, and usm_ndarrays for the number of repetitions. The basic approach, where repeats is a scalar, is implemented as _repeat_by_scalar in the _tensor_impl submodule. The more complicated case, where repeats is a tuple, is implemented as _repeat_by_sequence.

To implement _repeat_by_sequence, kernels for cumulative sums were moved into a separate header, and a 1D cumulative sum of general integers (rather than just nonzero) was added.

An example of the new functionality:

In [1]: import dpctl.tensor as dpt, numpy as np

In [2]: x = dpt.reshape(dpt.arange(5*10), (5, 10))

In [3]: x
Out[3]:
usm_ndarray([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
             [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
             [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
             [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
             [40, 41, 42, 43, 44, 45, 46, 47, 48, 49]])

In [4]: dpt.repeat(x, 2, axis=0)
Out[4]:
usm_ndarray([[ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
             [ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9],
             [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
             [10, 11, 12, 13, 14, 15, 16, 17, 18, 19],
             [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
             [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
             [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
             [30, 31, 32, 33, 34, 35, 36, 37, 38, 39],
             [40, 41, 42, 43, 44, 45, 46, 47, 48, 49],
             [40, 41, 42, 43, 44, 45, 46, 47, 48, 49]])

dpctl.tensor.tile is also implemented as as mostly top-level function.

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[github-actions]

View rendered docs @ https://intelpython.github.io/dpctl/pulls/1381/index.html

[coveralls]

coverage: 85.774% (+0.1%) from 85.65% when pulling 459d209 on repeat-impl into 51d994a on master.

[github-actions]

Array API standard conformance tests for dpctl=0.14.6dev4=py310ha25a700_40 ran successfully.
Passed: 915
Failed: 85
Skipped: 119

[oleksandr-pavlyk]

dpt.repeat(dpt.empty(tuple()), 2) requires to specify axis, but input arrays has none. Perhaps it is good for axis=None to also be allowed in this case.

[github-actions]

Array API standard conformance tests for dpctl=0.14.6dev4=py310ha25a700_41 ran successfully.
Passed: 916
Failed: 84
Skipped: 119

[github-actions]

Array API standard conformance tests for dpctl=0.14.6dev4=py310ha25a700_44 ran successfully.
Passed: 915
Failed: 85
Skipped: 119

[oleksandr-pavlyk]

Once we have tensor.min this could be made more efficient: dpt.min(repeats) >= 0

[oleksandr-pavlyk]

@ndgrigorian Since repeat argument can be rather large and, especially, if it were to be computed as usm_ndarray already, it is wasteful to force users to bring it to host and convert it to a tuple only to be copied back to usm_ndarray again.

I think we must support repeats parameter as usm_ndarray. A use case I have in mind is that the repeats sequence is a sample from a multinomial distribution.

[github-actions]

Array API standard conformance tests for dpctl=0.14.6dev5=py310ha25a700_10 ran successfully.
Passed: 916
Failed: 84
Skipped: 119

[oleksandr-pavlyk]

Thank you @ndgrigorian ! Look great.

[github-actions]

Deleted rendered PR docs from intelpython.github.com/dpctl, latest should be updated shortly. 🤞